# American Institute of Mathematical Sciences

doi: 10.3934/mcrf.2021017

## Second order directional shape derivatives of integrals on submanifolds

 Universität Bayreuth, 95440 Bayreuth, Germany

* Corresponding author: Anton Schiela

Received  February 2019 Revised  October 2019 Published  March 2021

Fund Project: This work was supported by DFG grant SCHI 1379/3-1

We compute first and second order shape sensitivities of integrals on smooth submanifolds using a variant of shape differentiation. The result is a quadratic form in terms of one perturbation vector field that yields a second order quadratic model of the perturbed functional. We discuss the structure of this derivative, derive domain expressions and Hadamard forms in a general geometric framework, and give a detailed geometric interpretation of the arising terms.

Citation: Anton Schiela, Julian Ortiz. Second order directional shape derivatives of integrals on submanifolds. Mathematical Control & Related Fields, doi: 10.3934/mcrf.2021017
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